1. Isosceles Triangle The two equal sides of an isosceles triangle are each 42
centimeters. If the base measures 30 centimeters, find the height and the
measure of the two equal angles. Round your answer to the nearest tenth.
Answers
Answer:
1. H = 29 cm
2. θ = 44°
Step-by-step explanation:
1. We can find the height of the triangle by considering the isosceles triangle as two right triangles. The height can be found by using Pitagoras:
\( L^{2} = H^{2} + B^{2} \)
Where:
L: is the sides of the isosceles triangle = 42 cm
B: is the base = 30 cm
H: is the height =?
Then, the height is:
\( H = \sqrt{L^{2} - B^{2}} = \sqrt{(42 cm)^{2} - (30 cm)^{2}} = 29.4 cm = 29 cm \)
2. The two equal angles (θ) can be found using the following trigonometric identity:
\( cos(\theta) = \frac{B}{L} \)
\( \theta = cos^{-1}(\frac{30 cm}{42 cm}) = 44.4^{\circ} = 44^{\circ} \)
Hence, the two equal angles are 44°.
I hope it helps you!
Related Questions
4) Ellen deposited $2,500 into a savings account
that earns 5% interest per year. Her friend's
bank offers a 6 1/2% annual interest rate. How
much more money would Ellen's money have
earned in one year if she had deposited her
money at her friend's bank?
A) $12.50
B) $32.50
C) $16.25
D) $37.50
Answers
Answer:
c
Step-by-step explanation:
(T & G) -> (E v D) what does this mean
Answers
Answer:
The work done by the electric field in Figure 1 to move a positive charge q from A, the positive plate, higher potential, to B, the negative plate, lower potential, is
W = −ΔPE = −qΔV.
The potential difference between points A and B is
−ΔV = −(VB − VA) = VA − VB = VAB.
Entering this into the expression for work yields W = qVAB.
Work is W = Fd cos θ; here cos θ = 1, since the path is parallel to the field, and so W = Fd. Since F = qE, we see that W = qEd. Substituting this expression for work into the previous equation gives qEd = qVAB.
The charge cancels, and so the voltage between points A and B is seen to be
{
V
AB
=
E
d
E
=
V
AB
d
(uniform E − field only)
Step-by-step explanation:
The relationship between V and E for parallel conducting plates is E=Vd E = V d. From a physicist's point of view, either ΔV or E can be used to describe any charge distribution
For which function defined by a
polynomial are the zeros of the
polynomial -3,0, and 4?
1) f(x)=(x+3)(x +4)
2) f(x)=(x² - 3)(x-4)
3) f(x)= x(x+3)(x-4)
4) f(x)= x(x − 3)(x +4)
Answers
Answer:
Option 3
Step-by-step explanation:
If we are given roots of a polynomial, r and q. We can represent the roots as
\((x - r)(x - q)\)
The roots here are 0, -3and 4 so the roots are
\(x(x - ( - 3)(x - 4)\)
Which equal to
\(x(x + 3)(x - 4)\)
Option 3 is the answer
Please help me with this proof.
Answers
Answer:
See below
Step-by-step explanation:
For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.
4.Does (3,-5) lie on the line y = -2x +1? Why or why not?5. Evaluate -y^2 – 2xy when x =-5 and y = 3.Can I get help with 4 and 5?
Answers
Question 4:
The equation of the line:
\(y\text{ = -2x+1}\)If the point (3, -5) lies on the line, when we substitute the x-value into the equation, we should have the given y-value.
Hence,
\(\begin{gathered} x\text{ = 3} \\ \text{Substitutitng:} \\ y=\text{ -2(3) + 1} \\ =\text{ -6 + 1} \\ =\text{ -5} \end{gathered}\)We can conclude that the point (3, -5) lies on the line.
Question 5
Given expression:
\(=-y^2-2xy\)Where:
x = -5 and y = 3:
Substituting we have:
\(\begin{gathered} =-3^2\text{ -2(-5)(3)} \\ =\text{ -9 +30} \\ =\text{ 21} \end{gathered}\)Answer: 21
Problem 1.(32 points) A random sample of 100 Uber rides in Chicago has on average 5.4miles per ride. Assume the distribution of the distance of Uber rides to be approximatelynormal with a standard deviation of 1.3 miles.(a) (5 points) Construct a 99% confidence interval for the average distance (in miles) ofan Uber ride. (round to one decimal place)(b) (4 points) What can we assert with 99% confidence about the possible size of our errorif we estimate the average distance of an Uber ride to be 5.4 miles
Answers
Answer:
a) CI = ( 5,1 ; 5,7 )
b) SE = 0,1
Step-by-step explanation:
a) Sample random n = 100
Mean = μ = 5,4
Standard deviation s = 1,3
CI = 99 % α = 1 % α = 0,01 α/2 = 0,005
z(c) for 0,005 is from z-table z(c) = 2,575
z(c) = ( X - μ ) /s/√n CI = μ ± z(c) * s/√n
CI = 5,4 ± 2,575* 1,3/10
CI = 5,4 ± 0,334
CI = ( 5,1 ; 5,7 )
b) SE = Standard deviation / √n
SE = 1,3 /10 SE = 0,1
We can support that with 99 % of probability our random variable will be in the CI.
g(a)= a^6- 5a
f(a)=–2a +5
Find g(f(a))
Answers
Answer:
(-2a+5)^6-5(-2a+5)
Step-by-step explanation:
plug f(a) into g(a) where there is an 'a'
The water level is 3 feet below your dock. The tide goes out, and the water level lowers 1 foot. A storm surge comes in, and the water level rises 2 feet. Write and integer to indicate the new water level.
Answers
Let f(x) = v= -6 and g(x) = 22 +5.(fog)(x) =m(gof)(x) =
Answers
Ok, so
Given:
\(\begin{gathered} f(x)=\sqrt[]{x}-6 \\ g(x)=x^2+5 \end{gathered}\)We want to find (fog)(x) and (gof)(x).
First, let's find (fog)(x).
This is:
\((fog)(x)=f(g(x))=f(x^2+5)\)So we're going to evaluate f in (x2 + 5).
\(f(x^2+5)=\sqrt[]{x^2+5}-6\)Now, let's find (gof)(x). This is:
\((gof)(x)=g(f(x))=g(\sqrt[]{x}-6)_{}\)So we're going to evaluate g in the function f.
\(g(\sqrt[]{x}-6)=(\sqrt[]{x}-6)^2+5\)………………………………… …………… ……..
Answers
Answer:
..... ........... ................. ...
Step-by-step explanation:
..............
....
.....
You roll a 6-sided die. What is P(even)?
Answers
what should be subtracted from 7/12+7/8 to obtain the multiplicated inverse of (4/3-4/9)
Answers
To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.
First, let's find the multiplicative inverse of (4/3 - 4/9):
Multiplicative inverse = 1 / (4/3 - 4/9)
To simplify the expression, we need a common denominator:
Multiplicative inverse = 1 / ((12/9) - (4/9))
= 1 / (8/9)
= 9/8
Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:
Subtracted value = (7/12 + 7/8) - (9/8)
To perform this calculation, we need a common denominator:
Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)
= (14/24 + 21/24) - (9/8)
= 35/24 - 9/8
To simplify further, we need a common denominator:
Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)
= 35/24 - 27/24
= 8/24
= 1/3
Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).
What is the measurement of these congruent angles ?
Answers
Answer:
x = 5 \ 65°
Step-by-step explanation:
(14(5)-5)° = (13(5))°
(70-5)° = 65°
65° = 65°
the measurement of the congruent angles are 65°
hope it's helpful :)))
Answer:
65°Step-by-step explanation:
What is the measurement of these congruent angles ?
14x - 5 = 13x
14x - 13x = 5
x = 5
-----------------------
check & angles
14 * 5 - 5 = 13 * 5
65 = 65
the answer is good
-----------------------------
In one hour, John can produce 20 loaves of bread or 18 cakes. In one hour, Phyllis can produce 30 loaves of bread or 15 cakes. Which of the following statements is true?
a. John has a comparative advantage in producing cakes.
b. Phyllis has an absolute advantage in both goods.
c. Phyllis has a comparative advantage in producing cakes.
d. John has an absolute advantage in both goods.
Answers
Correct Answer is c. Phyllis has a comparative advantage in producing cakes.
What is comparative advantage?
Comparative advantage is an economic concept that refers to the ability of an individual, firm, or country to produce a particular good or service more efficiently compared to others.
The opportunity cost of producing one cake for John is (20 loaves of bread) / (18 cakes) = 1.11 loaves of bread per cake.
The opportunity cost of producing one cake for Phyllis is (30 loaves of bread) / (15 cakes) = 2 loaves of bread per cake.
Since Phyllis has a lower opportunity cost of producing cakes (2 loaves of bread per cake) compared to John (1.11 loaves of bread per cake), Hence, Phyllis has a comparative advantage in producing cakes.
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Ali, Basti and Cian stand at three points A, B and C respectively. Suppose that the measure of angle ABC is 50 degrees , the measure of angle BAC is 60 degrees and Ali is exactly 150 ft away from Basti. Find the distance between Basti and Cian.
Answers
The distance between Basti and Cian is approximately 138.2 ft. Option D
To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.
Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.
Given:
Angle ABC = 50 degrees (angle opposite side AC)
Angle BAC = 60 degrees (angle opposite side BC)
Ali is 150 ft away from Basti (side AB)
We want to find the distance between Basti and Cian, which is side BC.
Using the Law of Sines, we have:
BC/sin(50) = AB/sin(60)
Substituting the known values:
BC/sin(50) = 150/sin(60)
To find BC, we can rearrange the equation:
BC = (150/sin(60)) * sin(50)
Using a calculator to evaluate the expression:
BC ≈ 138.2 ft
Option D is correct.
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The nth term of an AP is given by 2n +9 find the first term
Answers
Compute the required rate of return on two stocks with beta values of 0.5 and 2 respectively assuming the risk-
free rate of 5% and the market return of 10% using the capital asset pricing model. Please show work. Thank you.
Answers
The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.
What is Rate of return?Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.
What is stock?A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.
According to the given information:
The Capital Asset Pricing Model (CAPM) is expressed as:
R = Rf + beta*(Rm - Rf)
Where:
R = Required rate of return
Rf = Risk-free rate of return
beta = Beta coefficient (systematic risk)
Rm = Expected market return
Using the given values, we can compute the required rate of return for each stock:
Stock with beta of 0.5:
R = 5% + 0.5*(10% - 5%)
R = 7.5%
Stock with beta of 2:
R = 5% + 2*(10% - 5%)
R = 15%
Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.
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Henry's savings account has an APR of 3.65%, calculates interest daily, and
pays interest at the end of the month. If during the month of November, his
balance was $300 for the first 10 days of the month, $1200 for the next 10
days of the month, and $800 for the last 10 days of the month, how much
total interest did Henry earn in November?
Answers
First, we need to calculate the daily interest rate:
Daily interest rate = APR / 365 = 0.0365 / 365 = 0.0001
For the first 10 days, the interest earned on $300 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 300 x 0.0001 x 10 = $0.30
For the next 10 days, the interest earned on $1200 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 1200 x 0.0001 x 10 = $1.20
For the last 10 days, the interest earned on $800 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 800 x 0.0001 x 10 = $0.80
Therefore, the total interest earned by Henry in November is:
Total interest = $0.30 + $1.20 + $0.80 = $2.30
Therefore, Henry earned $2.30 interest in November.
7. How many solutions does the given system have?
y = 3x + 1
6x - 2y = -2
A. one solution
B. two solutions
C. infinite solutions
D. no solution
Answers
Answer:
C infinite solutions
Step-by-step explanation:
First, put both equations in the form of y=mx+b then you will get the same equation in both. Since both equations are the same they intersect at all the points which means this system has infinite solutions.
help meeeeeeeeee pleaseee !!!!!
Answers
The value of the composite function is determined as: (g o f)(5) = 6.
How to Determine the Value of a Composite Function?To determine the value of a composite function, first evaluate the inner function by plugging in the value of x given, then use the output of the inner function as an input to evaluate the outer function.
Given the following:
f(x) = x² - 6x + 2
g(x) = -2x
Therefore:
(g o f)(5) = g(f(5))
Find f(5):
f(5) = (5)² - 6(5) + 2
f(5) = 25 - 30 + 2
f(5) = -3
Find g(f(5)) by substituting x = -3 into g(x) = -2x:
g(f(5)) = -2(-3)
g(f(5)) = 6
Therefore, (g o f)(5) = 6.
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What do you get when you add 3 1/4 and 5 3/4?
2.
What is the answer to 6 2/3 + 5 3/4?
3.
How much is 18 – 4 1/5?
Answers
Answer:
HI THERE 1. is 9 2. is 7.08 and 3. is 13.8 pls mark brainlist
Step-by-step explanation:
Answer:
#1 is 9
#2 is 12 and 5/12
#3 is 69/5 or 13.8
PLSSSSSSSSSSSSSSS HELP pls
Answers
\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)
Let's solve ~
\(\qquad \sf \dashrightarrow \: 10x + 30 = 90\)
[ according to given figure ]
\(\qquad \sf \dashrightarrow \: 10x = 90 - 30\)
\(\qquad \sf \dashrightarrow \: 10x = 60\)
\(\qquad \sf \dashrightarrow \: x = 60 \div 10\)
\(\qquad \sf \dashrightarrow \: x = 6 \degree\)
Correct choice is D
Which one of these transformations would produce an image that is not congruent to its pre-image? (5 points) Group of answer choices A dilation followed by a reflection A rotation of 90 degrees about the origin A translation of (x − 1, y − 3) A rotation followed by a translation
Answers
The οptiοn “a dilatiοn fοllοwed by a reflectiοn” will prοduce an image that is nοt cοngruent tο its pre-image οptiοn, first οptiοn is cοrrect.
What is geοmetric transfοrmatiοn?It is defined as the change in cοοrdinates and the shape οf the geοmetrical bοdy. It is alsο referred tο as a twο-dimensiοnal transfοrmatiοn. In the geοmetric transfοrmatiοn, changes in the geοmetry can be pοssible by rοtatiοn, translatiοn, reflectiοn, and glide translatiοn.
As we knοw, the translatiοn will shift the οbject.
If rοtate the image with 90 degree abοut οrigin will change the οrientatiοn οf the image but shape will remains same.
A dilatiοn fοllοwed by reflectiοn will change the image because the transfοrmatiοn dilatiοn is used tο resize an item. Dilatiοn is a technique fοr making items appear larger οr smaller.
Thus, the οptiοn "a dilatiοn fοllοwed by a reflectiοn" will prοduce an image that is nοt cοngruent tο its pre-image οptiοn fοurth is cοrrect.
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Complete question:
Which one of these transformations would produce an image that is not congruent to its pre-image? (5 points)
[Group of answer choices]
A dilation followed by a reflection A rotation of 90 degrees about the origin A translation of (x − 1, y − 3) A rotation followed by a translation
assuming an interest rate of 5.4 percent, what is the value of the following cash flows four years from today? year cash flow 1 $ 3,000 2 4,040 3 5,885 4 7,975 multiple choice $23,120.48 $21,291.46 $22,178.61 $22,609.26 $23,631.70
Answers
The value of the cash flows four years from today is $22,609.26.
The value of a set of cash flows can be calculated using the present value of an annuity formula. This formula takes into account the time value of money, which states that money has a different value at different points in time due to the opportunity cost of the money. In other words, the money you have today is more valuable than the money you will have in the future.
The present value of an annuity formula is PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods. In this example, the cash flows are $3,000, $4,040, $5,885, and $7,975, the interest rate is 5.4%, and the number of periods is 4. Plugging these numbers into the formula, the present value is $22,609.26. This is the value of the cash flows four years from today.
The value of the cash flows four years from today is $22,609.26.
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Determine the value of f(4) given the function shown. *
f(x) = x² + 3
A. 19
B. -1
C. -5
D. -13
Answers
The value of function f (4) is,
⇒ f (4) = 19
We have to given that;
The function is,
⇒ f (x) = x² + 3
Now, WE can find the value of f (4) by substitute x = 4 in above function as,
⇒ f (x) = x² + 3
Plug x = 4;
⇒ f (4) = 4² + 3
⇒ f (4) = 16 + 3
⇒ f (4) = 19
Thus, The value of function f (4) is,
⇒ f (4) = 19
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Burning Brownie has five varieties of cakes as Chocolate fudge cake (Cake 1), Nutella-filled Cake (Cake 2), Marble Cake (Cake 3), Cheese cake (Cake 4) and Fruit Cake (Cake 5) at their store. The selling prices of each of the cakes are $9, $12, $4, $5, $8 respectively. a. Formulate the Revenue function If it takes 4 cups of milk, 7 cups of sugar, 1 egg, 3 cups flour & 4 cups cream to make Cake 1; 3 cups milk, 4 cups sugar, 2 egg, 4 cups flour & no cream to make Cake 2; 1 cups milk, 5 cups sugar, 3 eggs, 2 cups flour & 1 cup cream to make Cake 3; 5 cups milk, no sugar, 4 eggs, 4 cups flour & 5 cups cream for Cake 4; & lastly 4 cups milk, 8 cups sugar, 5 eggs, 6 cups flour & 3 cups cream to make Cake 5; Which types of cakes to be baked such that we get maximum Revenue? Keep in mind that the store has availability of maximum 280 cups milk, 300 cups sugar, 80 eggs, 250 cups flour & 190 cups cream at their disposal. b. Formulate the constraints of the scenario. c. Solve the system if linear inequalities using Excel Solver.
Answers
A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5
B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0
How did we get these values?To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:
a. Revenue Function:
Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.
The revenue function can be formulated as:
Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)
In equation form:
Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5
b. Constraints:
The constraints for the availability of ingredients can be formulated as follows:
Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280
Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300
Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80
Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250
Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190
Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0
c. Solve the system of linear inequalities using E x c e l Solver:
To solve the system of linear inequalities using E x c e l Solver, follow these steps:
1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:
| | A | B |
|-----|-----------|-----------------|
| 1 | Cakes | Selling Price |
| 2 | Cake 1 | $9 |
| 3 | Cake 2 | $12 |
| 4 | Cake 3 | $4 |
| 5 | Cake 4 | $5 |
| 6 | Cake 5 | $8 |
| | | |
| | | Formula |
| 9 | Milk | 280 |
| 10 | Sugar | 300 |
| 11 | Eggs | 80 |
| 12 | Flour | 250 |
| 13 | Cream | 190 |
2. In cell B16, enter the formula for the revenue:
=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11
3. In cell B18, enter the formula for the milk constraint:
=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6
4. In cell B19, enter the formula for the sugar constraint:
=7×B2 + 4×B3 + 5×B4
5. In cell B20, enter the formula for the egg constraint:
=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6
6. In cell B21, enter the formula for the flour constraint:
=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6
7. In cell B22, enter the formula for the cream constraint:
=4×B2 + 5×B4 + B5 + 3×B6
8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:
=B2
9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:
=B3
=B4
=B5
=B6
10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.
11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).
12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).
13. Click on the "Add" button in the "Subject to the Constraints" section.
14. In the Constraint window, select the range B18:B22 for the constraint cells.
15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.
16. Set the Solver options as desired, and click on the "Solve" button.
E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.
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The Language Arts department conducts a study to see if the number of books a student reads per month affects the score on the SAT Verbal Test. Here is the data that the Language Arts department collected for 8 students. Create the scatter plot for this data set. What is the equation of the line of best fit?
Answers
A scatter plot visually represents the relationship between two variables. It shows a positive correlation between the number of books read per month and SAT Verbal Test scores, with the equation y = 6.4828x + 520.6962.
A scatter plot is a graphical representation of a set of data that allows the observer to observe the relationship between two variables. It is used to graphically display how one variable is affected by the other. It is a chart of data points plotted on a two-dimensional graph with one variable represented on the X-axis and the other variable on the Y-axis.
Scatter Plot of the Data: From the data provided by the Language Arts department, we can create the scatter plot as shown below:
Equation of the line of best fit: The line of best fit is a straight line that is used to model the relationship between the two variables. It is determined by minimizing the sum of the squares of the differences between the observed values and the predicted values.
From the scatter plot, we can see that there is a positive correlation between the number of books read per month and the score on the SAT Verbal Test. This suggests that the more books a student reads per month, the higher their score on the SAT Verbal Test.
The equation of the line of best fit for the given data set is y = 6.4828x + 520.6962. Here, y represents the score on the SAT Verbal Test and x represents the number of books read per month.
To find the equation of the line of best fit, we can use a regression analysis tool such as Excel. The regression analysis will give us the values of the slope and intercept of the line of best fit, which we can use to write the equation of the line.
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A giant fish tank at the zoo contains z Halibut. The tank contains 4
times as many Bluefin Tuna as Halibut. Write an equation that
represents the total number of Bluefin Tuna, y in the tank.
Answers
Answer:
Y=4Z
Step-by-step explanation:
make a factorial story
Answers
Suppose that sec(t) = 3/2 and that t is in quadrant IV. Find the exact value of tan(t).
Answers
Using the trigonometric identities
\(\sec ^2(t)=\tan ^2(t)+1\)We want to find out the tan(t), then we can manipulate that formula and find tan(t) in function of sec(t).
\(\tan ^2(t)=\sec ^2(t)-1\)Now we can do square roots on both sides
\(\tan (t)=\pm\sqrt[]{\sec ^2(t)-1}\)We know that sec(t) = 3/2, then let's put it in our formula and simplify
\(\begin{gathered} \tan (t)=\pm\sqrt[]{\frac{3^2}{2^2}-1} \\ \\ \tan (t)=\pm\sqrt[]{\frac{9}{4}-1} \\ \\ \tan (t)=\pm\sqrt[]{\frac{9}{4}-\frac{4}{4}} \\ \\ \tan (t)=\pm\sqrt[]{\frac{5}{4}} \end{gathered}\)We can simplify and remove 4 from the square root, and we have
\(\tan (t)=\pm\frac{\sqrt[]{5}}{2}\)But which value is correct? the positive or the negative? Now we must use the information that the problem tells us, it says that t is in the quadrant IV, the tangent in quadrant IV is negative, then
\(\tan (t)=-\frac{\sqrt[]{5}}{2}\)